Optimization of water and land allocation in salinity and deficit- irrigation conditions at farm level in Qazvin plain

Improper extraction of water from resources especially in arid and semi-arid regions leads to a decrease in the quality of water and soil resources. In such areas, management activities such as increasing water productivity in agricultural sector would be a key step towards sustainable development. Therefore, water resources management to improve the allocation of limited water supplies is essential. In this study, a non-linear programming optimization model have been combined with a AquaCrop model to determine the optimal water and land allocation considering the quality issues of both water and soil resources with focusing on enhancing agriculture water productivity. For this purpose, the spatial variations of chemical and physical properties of soil in the Qazvin plain were taken into account. The soil of study site was divided into three salinity classes, and three weather conditions were identified by Standardized Precipitation Index (SPI). Moreover, five irrigation strategies were modeled under each weather condition. To understand the response of major crops under cultivation to water and salinity, the AquaCrop model was calibrated and validated (2005–2020) and utilized in the objective function. Accordingly, the production functions of the different products were obtained, and the cultivation area as well as amount of water consumption of the crops were optimized by using the target functions of maximum net income and maximum water use efficiency. The results showed that the model is capable of simulating crop yield in salinity and water deficit conditions. The coefficient of determination (R2) for barley, wheat and maize was equal to 0.86, 0.92, and 0.96, respectively. Findings reveal that total irrigation water could be reduced by 20% on average without profit reduction when compared to the profit of the present situation. Total economic profit could be increased by 18% on average through the optimization of water allocation and cropping pattern with the same water supply amount as that of the current situation. Also, the water productivity increased between 12 to 30% under these conditions. Therefore, the proposed model can efficiently optimize the amount of irrigation water and cultivation area on a regional scale considering salinity conditions.

Improper extraction of water from resources especially in arid and semi-arid regions leads to a decrease in the quality of water and soil resources. In such areas, management activities such as increasing water productivity in agricultural sector would be a key step towards sustainable development. Therefore, water resources management to improve the allocation of limited water supplies is essential. In this study, a non-linear programming optimization model have been combined with a crop model to determine the optimal water and land allocation considering the quality issues of both water and soil resources with focusing on enhancing agriculture water productivity. For this purpose, the spatial variations of chemical and physical properties of soil in the plain were taken into account. The soil of study site was divided into three salinity classes, and three weather conditions were identified by Standardized Precipitation Index (SPI). Moreover, five irrigation strategies were modeled under each weather condition. To understand the response of major crops under cultivation to water and salinity, the AquaCrop model was calibrated and validated (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020) and utilized in the objective function. Accordingly, the production functions of the different products were obtained, and the cultivation area as well as amount of water consumption of the crops were optimized by using the target functions of maximum net income and maximum water use efficiency. The results showed that the model is capable of simulating crop yield in salinity and water deficit conditions. The coefficient of determination (R 2 ) for barley, wheat and maize was equal to 0.86, 0.92, and 0.96, respectively. Findings reveal that total irrigation water could be reduced by 20% on average without profit reduction when compared to the profit of the present situation. Total economic profit could be increased by 18% on average through the optimization of water allocation and cropping pattern with the same water supply amount as that of the current situation. Also, the water productivity increased between 12 to 30% under these conditions. Therefore, the proposed model can efficiently optimize the amount of irrigation water and cultivation area on a regional scale considering salinity conditions.   Improper extraction of water from resources especially in arid and semi-24 arid regions leads to a decrease in the quality of water and soil resources. In 25 such areas, management activities such as increasing water productivity in 26 agricultural sector would be a key step towards sustainable development. 27 Therefore, water resources management to improve the allocation of limited 28 water supplies is essential. In this study, a non-linear programming 29 optimization model have been combined with a crop model to determine the 30 optimal water and land allocation considering the quality issues of both water 31 and soil resources with focusing on enhancing agriculture water productivity.

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For this purpose, the spatial variations of chemical and physical properties of 33 soil in the plain were taken into account. The soil of study site was divided 34 into three salinity classes, and three weather conditions were identified by   Also, the water productivity increased between 12 to 30% under these 51 conditions. Therefore, the proposed model can efficiently optimize the amount 52 of irrigation water and cultivation area on a regional scale considering salinity 53 conditions.

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Iran has always been facing water shortage due to its arid and semi-arid  The decline in the quality of water and arable soils in the region has led to 64 reduction in growth and production of agricultural products. It is essential to 65 use available water resources, including saline water, rationally and 66 sustainably, while to increase agricultural products. On the other hand, due to 67 the population growth it is necessary to provide food security adequately and   The simulation models can be linked with optimization approaches on 104 field scale: so they can also be applied to optimize irrigation scheduling, water    available in the area were simulated using the developed model (Fig 2). (1) Where Y x is the maximum yield (kg ha -1 ), Y is the real yield (kg ha -1 ), ET x 206 is the maximum evapotranspiration (mm), and ET is the real Where S i is the predicted value of yield (t ha -1 ) , O i is the measured value 279 of yield (t ha -1 ), n is the number of observations, and O is the mean measured  in Table 5.

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The highest value of NRMSE for calibration is 9.14 for Maize and the 304 lowest error is 5. 27  Crop water production functions (CWPFs) 332 The simulation results were used as a function of irrigation water after    of objective function i. The structure of payoff table is illustrated (Fig 3).

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Step 3 where P f and P u are the total benefits for the wet and dry years, respectively.

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Crop water production functions 445 For any economic analysis of irrigation water quantities, the production 446 functions give a mathematical relation between crop yield and irrigation water.

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The yield function (yield-seasonal irrigation) in each irrigation season (for 448 three years of wet, normal, dry year) for each of the 9 crop-soil units (three 449 soil types, for three crops of wheat, barley, and maize) was obtained using the 450 AquaCrop model (Fig 4). osmotic potential (Fig 4). As expected, the yield is higher in type I soils with conditions. In soils with higher salinity, water stress and salinity with adverse 478 effects on soil water potential energy and increase in osmotic pressure, cause 479 low crop growth, reduced water uptake by crops, and consequently, reduced 480 yield [12]. In general, the higher the salinity is, the lower the yield will be.  Under the present irrigation water supply, the optimized total benefit  (Table 7).

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It seems that the irrigation water has been first allocated to wheat from 5 537 water supply level, which is less than the maximum value of 438 mm at water 538 supply levels. The irrigation for the other two crops was also gradually 539 reduced from full irrigation to 40% deficit-irrigation (Table 7)  years. The amount of average irrigating for these wheat and barley was 260-544 155 mm and 371-199 mm, respectively form level IR1 to IR5 (Fig 6).   IR1  IR2  IR3  IR4  IR5  IR1  IR2  IR3  IR4  IR5  IR1  IR2  IR3  IR4  IR5   wet IR1  IR2  IR3  IR4  IR5  IR1  IR2  IR3  IR4  IR5  IR1  IR2  IR3  IR4  IR5   wet IR1  IR2  IR3  IR4  IR5  IR1  IR2  IR3  IR4  IR5  IR1  IR2  IR3  IR4  IR5   wet  the need for more production, the need for forage crops has also increased. As 567 shown in Table 7, by raising the cultivation area of products such as barley, 568 with aim of providing bread and animal feed, the profitability can be increased 569 in the province. Therefore, regarding the economic value of major crops, 570 wheat and barley are the two suggested crops for cultivation in the study area.

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Because of sensitivity to salinity, maize is not cultivated in very saline soils: 572 in soil with salinity of 4-8 ds/m, only 2% of cultivation is done.

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The area of crops as compared to present situation for wheat and maize  IR5 IR4 IR3 IR2 IR1  IR5 IR4 IR3 IR2 IR1  IR5 IR4 IR3 IR2 IR1   wet IR5 IR4 IR3 IR2 IR1  IR5 IR4 IR3 IR2 IR1  IR5 IR4 IR3 IR2 IR1   wet  The product price and producing cost are two important factors in optimal 587 water and land allocation. In this study, an attempt was made to optimize the 588 levels and amount of irrigation water with the two objectives of increasing 589 water productivity and increasing profit is shown in Fig 9. 590 As expected, in the case of reduced irrigation water and in all three soil 591 types, the profit decreased. As the soil salinity increased, the rate of reduction 592 in profit intensified. In very saline soils, this reduction was partial and 593 negligible up to 30% deficit-irrigation in wet weather conditions and up to 594 20% deficit-irrigation in dry weather conditions. In non-saline and saline soils, 595 a sharp reduction in profit occurred in the >30% deficit-irrigation scenarios.

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The results of the present study, like previous studies, indicate that the amount 597 of net profit in saline soils is affected by salinity; the higher soil salinity is, the 598 lower the final profit will be [16][17][18][19] That also reduces water productivity.
[34] also showed that water productivity increases by applying 600 deficit-irrigation. The increase in water productivity in all three soil types due 601 to deficit-irrigation is illustrated in Fig 8. According to Fig. 9, considering 602 reasonable variation in economic profit as compared in current situation, the 603 amount of profit at 20% of irrigation water stress were seen. At these levels, 604 the agricultural water productivity will be 20, 25, 31 % higher than those of 605 the full irrigation, respectively.    consumption to be about 10% less than full irrigation. The average irrigation 633 amount was reduced from 1256 to 1109 mm for optimal condition as 634 compared to present irrigation that decrease 12% and for level IR1-IR5, 635 decreased from 1109 to 685 mm for different climatic years.

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In this study, a regional economic optimization model was developed based